Geodesic
Multiplication modules over non-commutative rings
Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1837-1864

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It is proved that each submodule of a multiplication module over a regular ring is a multiplicative module. If $A$ is a ring with commutative multiplication of right ideals, then each projective right ideal is a multiplicative module, and a finitely generated $A$-module $M$ is a multiplicative module if and only if all its localizations with respect to maximal right ideals of $A$ are cyclic modules over the corresponding localizations of $A$. In addition, several known results on multiplication modules over commutative rings are extended to modules over not necessarily commutative rings. 
@article{SM_2003_194_12_a3,
     author = {A. A. Tuganbaev},
     title = {Multiplication modules over non-commutative rings},
     journal = {Sbornik. Mathematics},
     pages = {1837--1864},
     publisher = {mathdoc},
     volume = {194},
     number = {12},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_12_a3/}
}
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A. A. Tuganbaev. Multiplication modules over non-commutative rings. Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1837-1864. http://geodesic.mathdoc.fr/item/SM_2003_194_12_a3/